Assuming you were standing in the middle of the desert, and there were no hills or anything, and everything as far as you could see is flat. Assuming you had amazing superhuman vision, how far, in miles, could you see before the curve of the earth would impede vision?

It was beautiful out today, so I spent some time on the porch with the laptop and a tray table, and I saw a plane far off on the horizon. I figured it had to be five miles up in the air or so, and the sun was setting in the west, and I just sort of let my mind wander and was wondering how far away the plane must have been. How far could I see? Bonus rambling thoughts about the speed of light and how even if the speed of light is 186,000 mps, I was basically seeing the light reflecting off the plane instantaneously, even though it was probably several hundred miles away, because at 186k per second, this thing could be no more than a few hundred miles away, that basically means that the light from the reflection on the plane was there in a fraction of a fraction of a second. Plus, I know planes fly along the curve of the earth, so I just generally confused myself wondering just how far away the plane is. Then I started to wonder about how long it takes the light reflecting off all the things in my yard must take a billionth of a second or less to reach my eyes from ten feet away.

And this, my friends, is why I rarely work outside and prefer a room with no windows when I need to get things done.

” Assuming you were standing in the middle of the desert, and there were no hills or anything, and everything as far as you could see is flat. ”

Ans: between 2 to 4 miles, depending on how tall you are. I think 4 miles would take a really tall person. Probably about 3 miles on average.

If people think they can see lights 25 to 30 miles across a lake, then they are quite a bit higher than 6 feet above the surface, or a atmospheric conditions are bouncing light off the surface (Edit: or off air above the surface).

@A Ghost To Most: Interesting. When I’m on a boat in the Gulf or Atlantic, it is usually around the 12 mile mark when I lose sight of land/beach/dunes and only see structures..and that’s at deck level, I’m almost 6 feet tall.

I believe the true horizon line is only around 4 to 5 miles, maybe even less.

My calculation above was to the horizon.
But if the plane was 5 miles up that’s 26,400 feet. But 33,000 would be more likely.
Times 4/3 = about 35000.
So if it were 187 miles away it would appear to be on the horizon for you.

Theoretically. In practice your eyes can’t resolve something as small as a plane at that distance.
Think : resolving 1 minute of arc, so it depends on the size of the plane….

If you looked straight up, you could see many light-years. The Earth’s curvature only comes into play if you’re trying to see something just at the horizon. Atmospheric issues crop up as well (dust, etc.)

The horizon line crops up at about 5km(3 miles) for a human observer standing at sea level. If you’re at a higher elevation you can see further, as noted above. If you’re looking at a distant large/tall/high object, it can be much further away than 3 miles and be visible to you. Generally, the human eye’s ability to make out details fades at about a mile distance, though on a dark night you could probably still see a candle burning on the horizon.

This is why the transmitting antennas for services broadcasting at “line of sight” frequencies (read: TV) are so tall, and why an outside antenna 20..30 feet up helps so much as compared to rabbit ears 4 feet off the ground.

@Bob Munck: Hmmm. According to one of Wikipedia’s many many lists (naked-eye-visible galaxies), there are a few galaxies at about 10 mega lightyears distance which are barely visible to someone with good eyes and ideal viewing conditions. Anything further away from that, you need something with a bit more sensitivity than the Mk 1 eyeball to detect.

@p.a.:
And for the speed of thought, it takes about 1/100 of a second for the nerve impulses from the eye to reach the brain.

Bruce Lee once clocked his fastest punch at 3/100 of a second. Technically, that’s faster than the eye can typically see/process(1/24 of a second is pretty typical, which is why film runs at that speed).

Holden: You’re in a desert, walking along in the sand, when all of a sudden you look down…
Leon: What one?
Holden: What?
Leon: What desert?
Holden: It doesn’t make any difference what desert, it’s completely hypothetical.
Leon: But, how come I’d be there?
Holden: Maybe you’re fed up. Maybe you want to be by yourself. Who knows? You look down and see a tortoise, Leon. It’s crawling toward you…
Leon: Tortoise? What’s that?
Holden: [irritated by Leon’s interruptions] You know what a turtle is?
Leon: Of course!
Holden: Same thing.
Leon: I’ve never seen a turtle… But I understand what you mean.
Holden: You reach down and you flip the tortoise over on its back, Leon.
Leon: Do you make up these questions, Mr. Holden? Or do they write ’em down for you?
Holden: The tortoise lays on its back, its belly baking in the hot sun, beating its legs trying to turn itself over, but it can’t. Not without your help. But you’re not helping.
Leon: [angry at the suggestion] What do you mean, I’m not helping?
Holden: I mean: you’re not helping! Why is that, Leon?
[Leon has become visibly shaken]
Holden: They’re just questions, Leon. In answer to your query, they’re written down for me. It’s a test, designed to provoke an emotional response… Shall we continue?

I have read that in the movie “Enter the Dragon” the director asked Lee to slow down his punches because the camera was not catching it. He would punch and return in under a 24th of a second and it would look like he was just standing there. Pretty much like Gene Wilder’s hypothetical quick draw in “Blazing Saddles” (Do you want to see it again?).

as others have stated, not as great a distance as one might at first think.

The Verrazano Narrows Bridge (between Brooklyn and Staten Island) is so long (for a bridge) that engineers had to take the curvature of the earth into account when designing and building it.

The central span is less than a mile long, but the towers at either end of that central span are roughly 1½ inches farther apart at their tops than at their bottoms, the height of the towers being the factor which causes the small variance due to the Earth’s curvature.

Crow’s nests were put at the highest point of a sailing ship to increase the distance over the horizon the sailor could see. The could also see the top of the mast (not the hull) of an approaching ship at over 20 miles. Important during ocean combat.

Clearly you weren’t paying attention in science class when they taught the controversy: It’s important to consider the possibility that the earth is flat and that your “curve of the earth” notion is nonsense … in which case the answer to how far you could see is “infinity.” Unless, of course a frolicking sea monster at the end of the world was blocking your view. (ref. the upcoming “Godzilla” documentary.)

@OzarkHillbilly: My wife’s favorite movie of all time. I remember when we saw the first ‘Director’s Cut’ (without the narration). We were living in the wilds of Leonard, North Dakota (40 miles SW of Fargo) – which was rather a big change from her internship year in Washington D.C. (That has nothing to do with the movie, but the movie always sparks the memories.)

So that means that the relevant height for figuring this out is the elevation of the plane. If it is flying at 30k feet, it can see a long way. The Wiki page cited above says that if your elevation is 22k feet, you can see 184 miles. And a U2 at 70k feet can see well over 300 miles. So for a plane at 30k feet, 200 miles would be a decent estimate.

Actually depends on both how high you are and how high the airplane is. If your horizon is 3 miles and his is 100 miles, you can see him at a distance of 103 miles. Imagine the line of sight which goes from your eye to the plane, just grazing the edge of the earth.

One time riding a destroyer, I asked one of the lookouts how far he could see other ships from the lookout station (which is just off the bridge, a good ways up above the water line) and he said it was about 15 miles. There we’re talking about spotting the running lights of the other ship. I don’t know how far up the lights are.

I have a fair amount of experience with these calculations. I’ve written them into a lot of computer simulations.

The typically higher humidity in the east limits long range vision considerably. In the West when it is very dry and clear, you can see a little over 100 miles, but that is rare. I doubt that the plane was much over 50 miles

I think he must have dropped around when he typed ‘amazing super human vision ‘.

By the time he got to all the billions of eye-beams of like, EVERYTHING, all, like you know, dancing with each other on the way into, dude, like his very brain entangled with the ALL, in a billionth of TIME, myannn…. well, the acid was really starting to kick in.

Other people have mentioned the speed of light thing but here are a few science-y things about that to boggle your mind.

1. As somebody said upthread, light goes about 1 foot in a nanosecond. So while you’re looking around the room, reflect on how you don’t know what anything looks like NOW. You never do. All your news about what you see around you is nanoseconds old. And outside it’s even worse. If that plane was 300 km away, you were seeing where it was a millisecond ago. That’s a long time in some applications.

2. You measure the speed of light the way you measure anything else, by seeing how long it takes to go a specified distance. By around the 1980s, our ability to measure the time was so much better than our ability to measure the standard meter, that the meter was DEFINED in terms of light. Now light speed is 299,792,458 m/s by definition.

3. The GPS system accuracy depends on the system maintaining a world-wide time standard to within a few nanoseconds. But the satellites are thousands of miles away, many milliseconds of light travel. So when you, a GPS ground system, tell the satellite “set your clock to 2:00 right NOW” you have to say, in effect, “I don’t mean right now, I mean it was 2:00 when I said that but now it’s 2:00 and 3.483948 milliseconds by the time you’re reading this message…” That’s not how they really do it, but just think about the job of synchronizing clocks to an accuracy that is a tiny fraction of the time it takes your message to get there.

…there were no hills or anything, and everything as far as you could see is flat. Assuming you had amazing superhuman vision, how far, in miles, could you see before the curve of the earth would impede vision?

The curve of a sphere would never impede your horizontal vision unless you were standing on the inside surface of the sphere. I’m with the previous commenters that say you can see light years away when standing on the surface of an unfeatured earth.

@cathyx: It bugs the heck out of me that the entertainers of my childhood and youth are dropping off. Harold Ramis was a biggie. If they’re old, what does that make me?

Included in that are people like Billy Crystal making old-man jokes. He’s funny, but how can it be Billy freakin Crystal making these jokes? Jodie from Soap is an old fart? Miracle Max doesn’t count, that was makeup.

You kidding right? Hows that bunk working out for you? I love were I live but still do to medical problems a trip to town is the best I can do. Please get over it we are getting older and depend how you lived early you will do the time. I did everything wrong and don’t regret a minute of it, it’s Heeeell getting ooooold,

@Randy P: I always wondered how the battleships in WWII that could fire 20+ miles could determine where their misses landed. Seems they would need to be up quite high in the ship to see the water at that distance.

I was sitting across from a marina this afternoon, and I got to watching the boats and started to wonder: If the rungs on a ship’s ladder are 12″ apart and 1″ in diameter, and the tide is coming in at the rate of 3″ per minute, what is the minimum amount of time required for the tide to completely submerge three rungs?

@Randy P: It makes you old too. But you have to embrace the oldness. There’s nothing wrong with getting old except your body breaking down. That’s my big ‘getting old’ gripe.

I work with many young people and it bothers me that they never get any references from my youth or of any current political events. I can share current music with them and current celebrity news, but that’s it.

@gbear: I think he means, how far before something disappears over the edge. ‘Impeding’, because straight-line would need to bore through the earth to see it. It’s a correct, if uncommon way of looking at it.

Plans were made several years back to strip the Eiffel Tower before repainting, as it was determined that the combined weight of the paint from multiple repaintings was getting to be enough to put possibly dangerous strain and stress on structural integrity.

I remember the first time I visited the Eiffel Tower. I had convinced myself that it was just a tourist trap and probably overrated but I ended up loving it. The view from the top is spectacular and the construction is sort of mesmerizing. It reminded me of lacework made out of metal.

I was a Quartermaster in the Navy (a navigation person: supply is Army QM). The formulas above are correct, of course, but the thumb rule is “square root of the height of eye, plus one.” HOE in feet, distance in nautical miles (6075 feet).

If you are at the beach, assume your HOE (your height plus a little bit above the water) is 9 feet, so your distance to the horizon is 3+1, 4 NM. The formula given in Bowditch includes atmospheric refraction, and is “square root of height of eye(ft) x 1.17 = distance(NM)”, or 3.51NM for a 9ft HOE.

You do the same calculation for what you are looking at, and add the two together. If a ship’s superstructure is 49 ft high, it’s distance to the horizon is 7+1=8NM, plus your 4, so you can see it 12NM away. The ship would be “hull down,” meaning the waterline is past the horizon. The other terms are, “on the horizon” and “hull up.”

It’s nice to be able to comment for once on something I know (and damned hard not to be too prolix).

As long as they’re above the horizon and it’s night, you can probably see galaxies at least a million LY away.

The most distant galaxy people can credibly see naked-eye from a truly dark site on a clear, dry night is M33 (Triangulum), which is just over 3 million light-years away, and part of the “local group” of galaxies that includes our own Milky Way. The Andromeda galaxy (about 2.5 million light-years away) is the most distant galaxy people can usually see naked-eye under moderately dark skies affected to a mild extent by light pollution.

There are a few folks who have claimed to see another well-known galaxy M81 that is considered astronomically “bright” (about 8.5 million light years away), and M81 is easily viewable even in small-aperture amateur telescopes of 60mm or so – but frankly I call bullshit on such claims, based on how tiny an arc they span in a naked-eye view.

With telescopes, you can see Quasars (galaxies with extremely active, bright cores) that are over a billion light-years away, although the main value in viewing one is comes from contemplating the bizzarely exotic type of object it actually is, and the fact that your are viewing such ancient light coming from an object at such a staggeringly enormous distance – rather than because the physical appearance is very remarkable; they closely resemble just another unremarkable star.

I always wondered how the battleships in WWII that could fire 20+ miles could determine where their misses landed. Seems they would need to be up quite high in the ship to see the water at that distance.

@dmsilev:
Interesting wiki list.
Of the list of visible galaxies, the only full galaxy easily observable is Andromeda, 2.5 Mly. On a dark night I point it out to house guests if it is visible. (Approximately 1 trillion stars, but the central blob bright enough to see with human eyes is “only” several hundred billion stars. For the innumerate, mention that this is about over 1000 times the population of the U.S.. Drill down if necessary to a 100*100*100 (== 1 million) stack of soup cans.)
With a modestly big pair of binoculars (e.g. 7/50s, or 10/50s) some of the the other galaxies at 10+ Mly are easily seen.

I think this thread proves that even the educated public isn’t very good at scientific reasoning. Though the notion that it depends on your height which at least reflects the question asked (the hypothesis was a perfectly flat spherical surface, no Mt. Hoods etc., which seemed to elude many), came out fairly early. Lots of arguing from anecdotal experience, little from basic physical or mathematical principles.

@dmsilev, cmorenc: While I appreciate the information on visible galaxies, the point is that John was expecting an answer in the tens of miles; he was off by some 18 orders of magnitude. That’s the kind of error we normally see only in Republican budget proposals.

I don’t know if anyone has mentioned that Adm. Grace Hopper used to pass out what she called “nanoseconds,” pieces of wire about a foot long (that being the distance that light travels in a nanosecond). I once pointed out to her that the speed of light in copper is about .75C, meaning her wires should be 16 inches long. She told me to shut up.

@🍀 Martin: @dmsilev: @mike in dc: Oh, ffs, this what artillery does. Indirect fire. Shooting at things you can’t see. You need someone with a known location who calls in fire by any of variety of means, a fire direction center that can compute the data, and guns that can shoot using that data. Generally, one seeks a sheaf that brackets the target’ one, left; one, right; one beyond’ and one just short. You want to be within 50 m of the target when you ask for fire for effect.

In the interest of teaching a man to fish, here’s how you can work it out. Form a triangle between your eye (point E), the centre of the Earth (C) and the place where your line of sight disappears (D). The length CD is the radius of the Earth (R). The length CE is R+h, where h is the height of a John Cole. The unknown length is the length of DE, which let’s call L.

Now, here’s the trick. DE is tangent to the surface of the Earth, so DE and DC are at right angles. So we can use Pythagoras to say (R+h)^2=R^2+L^2; or R^2+2Rh+h^2=R^2+L^2.

Now, the R^2 terms cancel. The h^2 term doesn’t matter, since a John Cole is roughly six orders of magnitude smaller than the Earth. So we’ve got L^2=2Rh.

Then, 2R is the diameter of the Earth. The Earth is (by definition) 40000km in circumference, so its diameter is 4×10^7/pi. So take the stuff out of the square root sign that you can and you have L=2000 sqrt (10 h/pi). 10/pi is about 3, h is about 2 and the square root of six is about 2.5, so call it 5km plus or minus some small stuff to the horizon.

One League. Or as Wikipedia describes: “In nautical usage, a league of 3 nautical miles (5.5 km) is roughly how far an observer of average height (around 6 ft. or 1.8 m) can see when standing at sea level.”
Handy rule of thumb in the days of sail.

@oldster:shouldn’t the distance they can travel in a nanosecond be shorter?

Yeek! See, this is the reason I got out of physics and into Computer Science. Other than crashing the occasional Mars mission or undermining a major health insurance initiative, your stupid mistakes are much less visible in CS.

I hope I didn’t say the “should be 16 inches” part to Adm Grace; it’s a little too late to go find her and try to undo it.

@Viva BrisVegas: I’d have thought that the speed of light in copper was zero, since copper doesn’t transmit light.

It doesn’t transmit visible light, but some other kinds get through and are slowed by by the density of the medium. Gamma rays, for example. Gauge bosons in general. I think Hopper’s main point had to do with the length of her pieces of wire, not what they were made of. That’s why she told me to shut up.

Comments are closed.

Get Involved!

It takes just 5 minutes, twice a week:

Make a call
Send an email
Send a postcard or fax
Make your voice heard!

For both local and national numbers, recommended scripts and approaches: